The commonly accepted view is that the Universe is currently in the dark energy dominance era (estimated to start about 5 billion years ago)—the era where yet unknown dark energy dominates over the gravitation and is responsible for the observed acceleration of the Universe expansion. In the present paper, we consider a “gas” of a large number of gravitating neutral nonrelativistic particles having a practically infinite lifetime and zero or very little interaction with the rest of the matter (neutrinos could be an example). One of the central points is the application of Dirac’s Generalized Hamiltonian Dynamics to pairs of these particles. Another central point is the application of the virial theorem to pairs of zero total energy. We demonstrate that as a result, the gravitational interaction within the entire system effectively decreases. Together with the observational fact of the Universe rotation (according to Shamir’s study of 2020), this model provides a possible explanation of the entire history of the Universe expansion: both the era of the decelerating expansion and the current era of the accelerated expansion.
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